An idiom is an expression that is not meant to be taken literally. For example, in English, we often use the expression "It's raining cats and dogs". Obviously, we don't take this expression literally, we come to learn that it means it's raining hard outside.
Though the Chinese have many proverbs and idioms, Chengyu are formalized idioms, usually using only four characters and relating to folktales, classical literature, and historical accounts. The four characters typically state a moral, and in order to properly understand their meaning, it is important to know the story behind them. There are at least 5,000 Chengyu.
To learn about Chinese idioms is to gain another insight into the Chinese culture, their mores, and their history. We will be learning Chengyu, and their related stories, regularly for the rest of our "year in China". I believe the insights we'll gain will highlight many universal facets of human nature within their cultural context.